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      Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities

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          Abstract

          We generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of type 1/r(1,1,-1). We generalize furthermore the result of that to projective threefolds with only canonical singularities for canonical and not terminal singularities. It turns out that the estimates in the first three cases are better than the one for the smooth case, which it is not in the fourth case. We also give explicit examples which show the estimate in the fourth case is necessarily worse than the one for the smooth case.

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          On Fujita's freeness conjecture for 3-folds and 4-folds

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            Crepant Blowing-Up of 3-Dimensional Canonical Singularities and Its Application to Degenerations of Surfaces

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              Effective base point freeness

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                Author and article information

                Journal
                24 December 1998
                2000-04-17
                Article
                math/9812139
                8f6bd2f7-7999-4b15-b2d7-f60cf941e8ce
                History
                Custom metadata
                21 pages, Latex
                math.AG

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